ARCING OF CONTACTS IN TELEPHONE SWITCHING CIRCUITS 1235 



this case, however, in setting the boundary conditions one must consider 

 the drop in voltage across the main condenser during the previous 

 charging processes. The following are the resulting expressions for the 

 circuit current, main condenser voltage and the charging time, all as 

 functions of n: 



Kn) = -^^— . I n(l - a(n - 1 + an))\ (4a) 



V{n) = Fo - oLn{V, - v) (4b) 



„. tin) = sin- 4 , ; T + tan-' T-l^^^^^l'" (4c) 



Ll - a{n - 1)J L(l + oi)(n - 1)J 



Only an empirical expression for the summation 



Z tin) 

 was obtained with an error less than 10 per cent 

 i T o>-t(n) = Unf'\l + an). 



n=l ^ 



The current relation indicates that the current increases from zero 

 at n = to a maximum current 



1/2 



V'(0 



Sit an = }/2 then drops back to zero at na = 1.0 when the discharges 

 are terminated. The total discharge time is approximately ^{LCf^ and 

 the terminal voltage on the main condenser is Vct = v. If during the 

 process of current build-up the current reaches a value equal to the arc 

 initiation current a steady arc is established. It is evident that a steady 

 arc cannot be established if the maximum current attainable during 

 the discharges is less than the arc initiation current. This leads to the 

 concepts of a limiting inductance and Hmiting voltage in a circuit that 

 can allow the establishment of a steady arc.^ The limiting inductance is 



CONTACTS 



1 i 



^W^ 



C,Vo 



Fig. 2 — Typical condenser-inductance -contacts circuit. 



^ L. H. Germer, Arcing at Electrical Contacts on Closure, Part I, J. Appl. 

 Phys. 22, p. 955, 1951. 



